Question

In a certain residential suburb of 240 households, 120 use the TV, 130 the newspaper, and 140 the Internet to get their news. If 80 families use both the TV and the newspaper, 90 both the Internet and the newspaper, 70 the TV and the Internet, and 50 use all three, what proportion of households use exactly one source to get their news?

Answer 1

Answer: 0.25 proportion of households use exactly one source to get their news.

Step-by-step explanation:

Since we have given that

Number of household = 240

Number of households use TV = 120

Number of households use newspaper = 130

Number of households use internet = 140

Number of households use both TV and newspaper = 80

Number of households use both internet and newspaper = 90

Number of households use TV and internet = 70

Number of households use all three = 50

So, Number of households only use TV is given by

$120-(30+20+50)\\\\=120-100\\\\=20$

Number of households only use newspaper is given by

$130-(30+40+50)\\\\=130-120\\\\=10$

Number of households only use internet is given by

$140-(40+20+50)\\\\=140-110\\\\=30$

So, the proportion of households use exactly one source to get their news is given by

$\dfrac{20}{240}+\dfrac{10}{240}+\dfrac{30}{240}\\\\=\dfrac{60}{240}\\\\=0.25$

Hence, 0.25 proportion of households use exactly one source to get their news.